A Globally Convergent and Efficient Method for Unconstrained Discrete-Time Optimal Control

  • Authors:

  • Chi Kong Ng;Li-Zhi Liao;Duan Li

  • Affiliations:

  • Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China. (E-mail: ckng@se.cuhk.edu.hk);Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China.Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shati ...;Corresponding author. (e-mail: liliao@hkbu.edu.hk)

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2002

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Abstract

Shift schemes are commonly used in non-convex situations when solving unconstrained discrete-time optimal control problems by the differential dynamic programming (DDP) method. However, the existing shift schemes are inefficient when the shift becomes too large. In this paper, a new method of combining the DDP method with a shift scheme and the steepest descent method is proposed to cope with non-convex situations. Under certain assumptions, the proposed method is globally convergent and has q-quadratic local conve rgence. Extensive numerical experiments on many test problems in the literature are reported. These numerical results illustrate the robustness and efficiency of the proposed method.